MathDB
1st ibmo - colombia 1985./q6

Source: Spanish Communities

April 6, 2006
Columbiageometrycircumcircletrigonometrygeometry unsolved

Problem Statement

Given an acute triangle ABCABC, let DD, EE and FF be points in the lines BCBC, ACAC and ABAB respectively. If the lines ADAD, BEBE and CFCF pass through OO the centre of the circumcircle of the triangle ABCABC, whose radius is RR, show that: \frac{1}{AD}\plus{}\frac{1}{BE}\plus{}\frac{1}{CF}\equal{}\frac{2}{R}